City charters offer more extensive rights than town charters (and generally speaking, if a city had a city charter, it would include the rights of a town charter but not vice-versa). So for example, a town charter might provide borough rights (i.e, its inhabitants are burghers not peasants) and some measure of self-government but only a city charter would give you the staple or storage right (which was necessary to conduct international trade). a town charter might give you the right to hold a market but you might need a city charter to the right to establish a warehouse (which was very important for long-distance, international, and bulk trade). 

In terms of how a charter affects the residents of a town, it provided a whole host of legal, political, and economic opportunities that could change one’s status enormously. Being a burgher meant that you not only had the right to live in the town, but that you were a free person under the law and not a serf. Living in a chartered town or city probably meant that there were guilds you could join and become a member of, and it definitely meant access to markets and trade and occupations that could not be accessed outside of that town/city. It might mean that there was a city government that you could vote for or run for office in if you got wealthy enough. 

While there are cases of charters being granted ahead of construction – often as a means of enticing people to move to a new (and therefore risky) settlement – usually, the settlement would predate the charter. The way it normally worked is that you had a settlement of people who would petition the king or overlord for a charter, the charter would be written out and sealed (as we see above), and there would be a big ceremony where the king/overlord would present the charter to the city government, after which the city would now exist as a legal corporation.